Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6803     4993.8                                 
## 2   6802     4979.5  1  14.368  19.626 9.565e-06 ***
## 3   6801     4700.1  1 279.362 404.233 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24896.15
## 2     2 24878.54
## 3     3 24487.57

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.002313   0.142295   0.016    0.987    
## phi   0.019566   0.004338   4.510 6.58e-06 ***
## alpha 0.631937   0.029466  21.447  < 2e-16 ***
## A     3.689310   0.107156  34.429  < 2e-16 ***
## k     9.801095   0.673936  14.543  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8313 on 6801 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.761e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_211,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6801     4700.1                              
## 2   6800     4695.2  1 4.9446  7.1613 0.007467 **
## 3   6799     4694.0  1 1.1736  1.6998 0.192352   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 24487.57
## 2    3a 24482.41
## 3    3b       NA
## 4    3c 24482.71

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.003234   0.142270   0.023  0.98186    
## phi    0.019635   0.004338   4.526  6.1e-06 ***
## alpha  0.630429   0.029469  21.393  < 2e-16 ***
## A      3.741260   0.112468  33.265  < 2e-16 ***
## k     13.699719   2.063458   6.639  3.4e-11 ***
## p      0.147297   0.051078   2.884  0.00394 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8309 on 6800 degrees of freedom
## 
## Number of iterations to convergence: 3 
## Achieved convergence tolerance: 5.436e-06

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 250 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 250 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1259 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  18772      15066                                  
## 2  18767      14987  5   79.84   19.997 < 2.2e-16 ***
## 3  18766      13948  1 1038.75 1397.574 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 64126.34
## 2     2 64018.45
## 3     3 62672.11

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.613447   0.124463   4.929 8.35e-07 ***
## phi    0.029034   0.002734  10.620  < 2e-16 ***
## alpha  0.822583   0.020204  40.714  < 2e-16 ***
## A      2.880787   0.064092  44.948  < 2e-16 ***
## k     13.763371   0.481140  28.606  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8621 on 18766 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.821e-06
##   (4 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18766      13948                                 
## 2  18765      13790  1 157.965 214.957 < 2.2e-16 ***
## 3  18765      13818  0   0.000                      
## 4  18764      13790  1  28.524  38.814 4.762e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 62672.11
## 2    3a 62460.31
## 3    3b 62499.01
## 4    3c 62462.22

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.587555   0.122541   4.795 1.64e-06 ***
## phi    0.029607   0.002709  10.928  < 2e-16 ***
## alpha  0.814647   0.020054  40.623  < 2e-16 ***
## A      3.134793   0.075777  41.369  < 2e-16 ***
## k     29.206857   1.949741  14.980  < 2e-16 ***
## p      0.193257   0.010655  18.138  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8572 on 18765 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 4.74e-06
##   (4 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 715 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 715 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1316 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   7159     7630.8                               
## 2   7158     7627.7  1   3.01   2.8274 0.09271 .  
## 3   7157     7278.5  1 349.23 343.3965 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29878.52
## 2     2 29877.69
## 3     3 29544.04

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.406513   0.084819 -16.582   <2e-16 ***
## phi    0.006082   0.004503   1.351    0.177    
## alpha  0.687050   0.034952  19.657   <2e-16 ***
## A      6.236216   0.163606  38.117   <2e-16 ***
## k     19.977711   1.683017  11.870   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.008 on 7157 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.992e-06
##   (8 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7157     7278.5                                
## 2   7156     7212.0  1 66.481  65.964 5.366e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 29544.04
## 2    3a 29480.33
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.435366   0.083176 -17.257  < 2e-16 ***
## phi    0.006702   0.004483   1.495    0.135    
## alpha  0.685682   0.034486  19.883  < 2e-16 ***
## A      7.601341   0.369404  20.577  < 2e-16 ***
## k     99.330652  19.960728   4.976 6.63e-07 ***
## p      0.330195   0.020993  15.729  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.004 on 7156 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 5.435e-06
##   (8 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 253 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 255 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1238 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1   4867     3972.7                                  
## 2   4866     3964.9  1   7.849   9.6331  0.001922 ** 
## 3   4865     3691.1  1 273.807 360.8898 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18011.57
## 2     2 18003.94
## 3     3 17657.45

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.367163   0.173787  -2.113  0.03468 *  
## phi    0.021679   0.007424   2.920  0.00352 ** 
## alpha  0.800963   0.038568  20.768  < 2e-16 ***
## A      4.975276   0.181412  27.425  < 2e-16 ***
## k     31.602813   1.879517  16.814  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.871 on 4865 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.407e-06
##   (7 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4865     3691.1                                
## 2   4864     3599.1  1 91.936  124.25 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17657.45
## 2    3a 17536.62
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.383203   0.170237  -2.251   0.0244 *  
## phi     0.018160   0.007244   2.507   0.0122 *  
## alpha   0.792487   0.038011  20.849  < 2e-16 ***
## A       6.608906   0.369952  17.864  < 2e-16 ***
## k     112.210544  14.732460   7.617 3.11e-14 ***
## p       0.179723   0.010121  17.758  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8602 on 4864 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.696e-06
##   (7 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95673, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -16, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 184 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 185 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1280 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8777     8518.0                                 
## 2   8776     8502.7  1  15.249  15.739 7.329e-05 ***
## 3   8775     8242.9  1 259.861 276.637 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 34239.99
## 2     2 34226.26
## 3     3 33955.74

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.38661    0.08275  -16.76  < 2e-16 ***
## phi   -0.02233    0.00542   -4.12 3.83e-05 ***
## alpha  0.64066    0.03630   17.65  < 2e-16 ***
## A      6.47289    0.18128   35.71  < 2e-16 ***
## k     42.04372    2.70957   15.52  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9692 on 8775 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.628e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 33955.74
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.38661    0.08275  -16.76  < 2e-16 ***
## phi   -0.02233    0.00542   -4.12 3.83e-05 ***
## alpha  0.64066    0.03630   17.65  < 2e-16 ***
## A      6.47289    0.18128   35.71  < 2e-16 ***
## k     42.04372    2.70957   15.52  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9692 on 8775 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.628e-06
##   (3 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 332 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 334 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1298 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq   F value Pr(>F)    
## 1  12343      22303                                
## 2  12342      22302  1    0.39    0.2176 0.6409    
## 3  12341      19979  1 2323.23 1435.0642 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60705.76
## 2     2 60707.54
## 3     3 59351.41

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.164562   0.098508  -1.671   0.0948 .  
## phi   -0.002456   0.004112  -0.597   0.5504    
## alpha  0.842236   0.020224  41.645   <2e-16 ***
## A      5.423448   0.112581  48.174   <2e-16 ***
## k      2.780933   0.247040  11.257   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.272 on 12341 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.199e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12341      19979                                
## 2  12340      19891  1 87.674 54.3911 1.748e-13 ***
## 3  12340      19902  0  0.000                      
## 4  12339      19891  1 10.595  6.5722   0.01037 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 59351.41
## 2    3a 59299.11
## 3    3b 59305.61
## 4    3c 59301.03

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.186851   0.097467  -1.917   0.0553 .  
## phi   -0.002130   0.004095  -0.520   0.6029    
## alpha  0.840183   0.020110  41.780  < 2e-16 ***
## A      5.596113   0.122987  45.502  < 2e-16 ***
## k      8.774600   1.622335   5.409 6.47e-08 ***
## p      0.390472   0.040679   9.599  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.27 on 12340 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.029e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 481 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 481 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1261 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq   F value Pr(>F)    
## 1  12467      26614                                
## 2  12466      26612  1    2.65    1.2433 0.2649    
## 3  12465      24215  1 2396.31 1233.5227 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 61666.13
## 2     2 61666.88
## 3     3 60492.17

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -0.2628008  0.1112158  -2.363   0.0181 *  
## phi   -0.0005468  0.0045482  -0.120   0.9043    
## alpha  0.8349426  0.0213640  39.082   <2e-16 ***
## A      5.4202590  0.1350753  40.128   <2e-16 ***
## k      8.0094796  0.4943964  16.201   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.394 on 12465 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.591e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  12465      24215                                 
## 2  12464      23985  1 229.888 119.462 < 2.2e-16 ***
## 3  12464      24056  0   0.000                      
## 4  12463      23974  1  81.719  42.482 7.407e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 60492.17
## 2    3a 60375.22
## 3    3b 60411.70
## 4    3c 60371.26

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -0.2904340  0.1092242  -2.659  0.00785 ** 
## phi   -0.0008326  0.0045073  -0.185  0.85345    
## alpha  0.8287948  0.0211994  39.095  < 2e-16 ***
## A      5.5132325  0.1680533  32.806  < 2e-16 ***
## k     24.1803371  2.1461877  11.267  < 2e-16 ***
## s      1.3906668  0.1759005   7.906 2.88e-15 ***
## p      0.3791942  0.0308751  12.282  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.387 on 12463 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.006e-06

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 486 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 486 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1247 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1262     2732.4                              
## 2   1261     2730.8  1   1.616  0.7464 0.3878    
## 3   1260     2575.7  1 155.141 75.8939 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6239.319
## 2     2 6240.570
## 3     3 6168.582

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.59312    1.11801   1.425    0.154    
## phi   -0.02501    0.02078  -1.204    0.229    
## alpha  0.77337    0.08005   9.662  < 2e-16 ***
## A      3.62885    0.63193   5.742 1.17e-08 ***
## k      9.60975    2.31023   4.160 3.40e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.43 on 1260 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.275e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': p
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1260     2575.7                         
## 2   1259     2570.8  1 4.9103  2.4048 0.1212
##   model      AIC
## 1     3 6168.582
## 2    3a 6168.168
## 3    3b 6168.069
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.60921    1.12275   1.433  0.15203    
## phi   -0.02576    0.02078  -1.240  0.21524    
## alpha  0.76892    0.08010   9.599  < 2e-16 ***
## A      4.13842    0.92838   4.458 9.02e-06 ***
## k     11.64559    6.19571   1.880  0.06039 .  
## s      0.61393    0.21272   2.886  0.00397 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.429 on 1259 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.098e-06

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95842, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.9898, p-value = 6.612e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 48 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 48 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1224 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1     77     67.216                              
## 2     76     66.744  1 0.4721  0.5376 0.465679   
## 3     75     59.184  1 7.5601  9.5805 0.002764 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 355.9610
## 2     2 357.3970
## 3     3 349.7798

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.29976    1.83293  -0.164 0.870533    
## phi    0.06367    0.05197   1.225 0.224338    
## alpha  0.86978    0.25121   3.462 0.000888 ***
## A      7.68709    3.17610   2.420 0.017929 *  
## k     30.51595   12.20049   2.501 0.014559 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8883 on 75 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.21e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_242,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_242,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1     75     59.184                              
## 2     74     51.768  1 7.4154    10.6 0.001707 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 349.7798
## 2    3a 341.0704
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)   
## ge      -0.95258    1.30354  -0.731  0.46723   
## phi      0.06990    0.04843   1.443  0.15318   
## alpha    0.81225    0.24162   3.362  0.00123 **
## A       22.29721   27.51039   0.811  0.42025   
## k     1188.98715 2351.33832   0.506  0.61460   
## p        0.20353    0.20959   0.971  0.33468   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8364 on 74 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 3.221e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98698, p-value = 0.5974
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.45007, p-value = 0.6527
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 903 row(s) containing missing values (geom_path).

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1793     1540.0                                 
## 2   1792     1534.1  1  5.9178  6.9128  0.008631 ** 
## 3   1791     1520.8  1 13.2245 15.5735 8.242e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6619.016
## 2     2 6614.101
## 3     3 6600.552

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.74029    0.26671  -2.776  0.00557 ** 
## phi    0.02494    0.01059   2.356  0.01858 *  
## alpha  0.37760    0.09201   4.104 4.24e-05 ***
## A      4.23533    0.27361  15.480  < 2e-16 ***
## k     22.62163    3.11717   7.257 5.86e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9215 on 1791 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.487e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1791     1520.8                                
## 2   1790     1470.0  1 50.831  61.895 6.215e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6600.552
## 2    3a 6541.499
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      -0.82489    0.25083  -3.289  0.00103 ** 
## phi      0.02636    0.01038   2.540  0.01117 *  
## alpha    0.39463    0.08826   4.471 8.26e-06 ***
## A       19.86974   24.80713   0.801  0.42326    
## k     1228.26934 1975.51782   0.622  0.53419    
## p        0.10447    0.12488   0.836  0.40299    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9062 on 1790 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 7.715e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91943, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -10.734, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 72 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 72 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1309 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    151     542.82                          
## 2    150     542.67  1 0.14635  0.0405 0.8409
## 3    149     539.56  1 3.11479  0.8602 0.3552
##   model      AIC
## 1     1 926.7454
## 2     2 928.7038
## 3     3 929.8174

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge  -1.5581     1.1263  -1.383  0.16858   
## A    8.5930     2.9492   2.914  0.00412 **
## k   -0.2271     4.9099  -0.046  0.96316   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.896 on 151 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 6.84e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     1 926.7454
## 2    1a       NA
## 3    1b       NA
## 4    1c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge  -1.5581     1.1263  -1.383  0.16858   
## A    8.5930     2.9492   2.914  0.00412 **
## k   -0.2271     4.9099  -0.046  0.96316   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.896 on 151 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 6.84e-06
##   (1 observation deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95653, p-value = 9.534e-05
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.64899, p-value = 0.5163
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 6 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1884 row(s) containing missing values (geom_path).

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    211    105.125                              
## 2    210    103.499  1 1.6256  3.2983 0.070777 . 
## 3    209     99.344  1 4.1559  8.7433 0.003465 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 498.6817
## 2     2 497.3467
## 3     3 490.5764

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge     -1.11494    0.99312  -1.123  0.26287   
## phi    -0.09677    0.07116  -1.360  0.17533   
## alpha   0.81661    0.24529   3.329  0.00103 **
## A       3.47187    1.19369   2.909  0.00402 **
## k     111.42030   36.72779   3.034  0.00272 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6894 on 209 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.769e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    209     99.344                            
## 2    208     96.499  1 2.8448  6.1318 0.01408 *
## 3    207     94.551  1 1.9482  4.2652 0.04015 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 490.5764
## 2    3a 486.3589
## 3    3b       NA
## 4    3c 483.9944

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.15472    0.94108  -1.227 0.221211    
## phi    -0.09545    0.06806  -1.402 0.162311    
## alpha   0.84400    0.23481   3.594 0.000406 ***
## A       2.68538    0.91529   2.934 0.003725 ** 
## k     109.84363   26.18684   4.195 4.05e-05 ***
## s       2.81887    1.33665   2.109 0.036155 *  
## p       0.31531    0.09800   3.218 0.001501 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6758 on 207 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.874e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97558, p-value = 0.0009008
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.018123, p-value = 0.9855
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 8 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 8 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1272 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    191     153.88                              
## 2    190     153.65  1 0.2322  0.2871 0.592712   
## 3    189     148.00  1 5.6458  7.2097 0.007896 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 616.7039
## 2     2 618.4110
## 3     3 613.1482

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.18048    1.41956   0.127  0.89896   
## phi    0.02621    0.03238   0.809  0.41926   
## alpha  0.74146    0.24974   2.969  0.00338 **
## A      4.26017    1.31891   3.230  0.00146 **
## k     73.68572   23.20341   3.176  0.00175 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8849 on 189 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.194e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    189     148.00                            
## 2    188     145.01  1 2.9971  3.8857 0.05017 .
## 3    188     146.37  0 0.0000                  
## 4    187     144.47  1 1.8955  2.4534 0.11896  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 613.1482
## 2    3a 611.1793
## 3    3b 612.9933
## 4    3c 612.4646

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge      0.26182    1.44312   0.181  0.85623   
## phi     0.02425    0.03187   0.761  0.44773   
## alpha   0.71025    0.25011   2.840  0.00501 **
## A       5.21576    2.01157   2.593  0.01027 * 
## k     142.59856   82.12245   1.736  0.08413 . 
## p       0.07450    0.03154   2.362  0.01918 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8782 on 188 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.058e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87217, p-value = 9.607e-12
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.9762, p-value = 0.04814
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 10 rows containing missing values (geom_point).

## Warning: Removed 1308 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    112     64.762                                
## 2    111     64.757  1 0.0050  0.0086 0.9262372    
## 3    110     58.505  1 6.2514 11.7538 0.0008554 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 281.0948
## 2     2 283.0859
## 3     3 273.4110

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      2.664552   6.035725   0.441 0.659744    
## phi    -0.001369   0.049853  -0.027 0.978140    
## alpha   0.882084   0.226696   3.891 0.000171 ***
## A       3.485949   2.914237   1.196 0.234199    
## k     119.510749  46.346783   2.579 0.011240 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7293 on 110 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.475e-06
##   (6 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_342,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_342,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    110     58.505                          
## 2    109     58.268  1 0.23753  0.4443 0.5064
##   model      AIC
## 1     3 273.4110
## 2    3a 274.9432
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      2.664552   6.035725   0.441 0.659744    
## phi    -0.001369   0.049853  -0.027 0.978140    
## alpha   0.882084   0.226696   3.891 0.000171 ***
## A       3.485949   2.914237   1.196 0.234199    
## k     119.510749  46.346783   2.579 0.011240 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7293 on 110 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.475e-06
##   (6 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9253, p-value = 7.497e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.5772, p-value = 0.009961
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (geom_point).

plotting 2

411 - Everglades

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6726     4643.6                                
## 2   6725     4629.4  1  14.19  20.609 5.732e-06 ***
## 3   6724     4292.9  1 336.46 526.988 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24169.66
## 2     2 24151.07
## 3     3 23645.34

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.561222   0.172710   3.249 0.001162 ** 
## phi   0.013736   0.003985   3.447 0.000571 ***
## alpha 0.652872   0.026435  24.697  < 2e-16 ***
## A     3.091045   0.104099  29.693  < 2e-16 ***
## k     3.644354   0.420767   8.661  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.799 on 6724 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.867e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6724     4292.9                                
## 2   6723     4289.6  1 3.3301  5.2192 0.0223693 *  
## 3   6723     4292.7  0 0.0000                      
## 4   6722     4284.7  1 7.9936 12.5406 0.0004009 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 23645.34
## 2    3a 23642.11
## 3    3b 23647.01
## 4    3c 23636.47

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.551036   0.171824   3.207 0.001348 ** 
## phi    0.013969   0.003984   3.506 0.000457 ***
## alpha  0.652137   0.026377  24.724  < 2e-16 ***
## A      3.030047   0.102675  29.511  < 2e-16 ***
## k     11.469522   2.059551   5.569 2.66e-08 ***
## p      0.434424   0.064905   6.693 2.36e-11 ***
## s      1.831085   0.364824   5.019 5.33e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7984 on 6722 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.677e-06

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 239 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 239 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1268 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   8031      11168                               
## 2   8030      11166  1   1.823   1.3112 0.2522    
## 3   8029      10911  1 254.340 187.1516 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35928.80
## 2     2 35929.49
## 3     3 35746.37

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.745755   0.108485  -6.874 6.70e-12 ***
## phi   -0.004038   0.005576  -0.724    0.469    
## alpha  0.706276   0.049224  14.348  < 2e-16 ***
## A      5.088125   0.146783  34.664  < 2e-16 ***
## k     13.204274   1.640594   8.048 9.58e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.166 on 8029 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.523e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 35746.37
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.745755   0.108485  -6.874 6.70e-12 ***
## phi   -0.004038   0.005576  -0.724    0.469    
## alpha  0.706276   0.049224  14.348  < 2e-16 ***
## A      5.088125   0.146783  34.664  < 2e-16 ***
## k     13.204274   1.640594   8.048 9.58e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.166 on 8029 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.523e-06

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 306 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 306 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1227 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    880     1100.5                                
## 2    879     1098.3  1  2.201  1.7611    0.1848    
## 3    878     1056.4  1 41.982 34.8937 4.976e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3499.284
## 2     2 3499.516
## 3     3 3467.103

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.75733    1.43670   1.919   0.0553 .  
## phi   -0.04134    0.02218  -1.864   0.0627 .  
## alpha  0.90068    0.14067   6.403 2.48e-10 ***
## A      2.04112    0.39553   5.160 3.05e-07 ***
## k     14.57963    6.08332   2.397   0.0168 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.097 on 878 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 8.927e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 3467.103
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.75733    1.43670   1.919   0.0553 .  
## phi   -0.04134    0.02218  -1.864   0.0627 .  
## alpha  0.90068    0.14067   6.403 2.48e-10 ***
## A      2.04112    0.39553   5.160 3.05e-07 ***
## k     14.57963    6.08332   2.397   0.0168 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.097 on 878 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 8.927e-06

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96591, p-value = 1.666e-13
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.1402, p-value = 0.03234
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 30 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 30 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1313 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    984     1380.5                                
## 2    983     1362.3  1 18.220  13.147 0.0003028 ***
## 3    982     1318.1  1 44.205  32.933  1.27e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4121.784
## 2     2 4110.671
## 3     3 4080.114

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.59998    1.21002   1.322   0.1864    
## phi    0.06577    0.02558   2.571   0.0103 *  
## alpha  0.72924    0.11866   6.146 1.16e-09 ***
## A      2.18045    0.41408   5.266 1.72e-07 ***
## k      3.19690    1.48910   2.147   0.0320 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.159 on 982 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.242e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 4080.114
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.59998    1.21002   1.322   0.1864    
## phi    0.06577    0.02558   2.571   0.0103 *  
## alpha  0.72924    0.11866   6.146 1.16e-09 ***
## A      2.18045    0.41408   5.266 1.72e-07 ***
## k      3.19690    1.48910   2.147   0.0320 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.159 on 982 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.242e-06
##   (1 observation deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93491, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.094, p-value = 1.101e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 39 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 39 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1321 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3153     5953.4                                
## 2   3152     5925.9  1  27.58  14.672 0.0001304 ***
## 3   3151     5607.9  1 318.01 178.685 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14761.88
## 2     2 14749.22
## 3     3 14577.14

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.16625    0.29272  -3.984 6.93e-05 ***
## phi   -0.05013    0.01571  -3.192  0.00143 ** 
## alpha  0.97943    0.06623  14.788  < 2e-16 ***
## A      8.24024    0.70911  11.621  < 2e-16 ***
## k     87.52750    6.33761  13.811  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.334 on 3151 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.72e-06
##   (23 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3151     5607.9                                
## 2   3150     5532.1  1 75.782  43.151 5.906e-11 ***
## 3   3150     5563.3  0  0.000                      
## 4   3149     5509.3  1 53.962  30.843 3.030e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 14577.14
## 2    3a 14536.20
## 3    3b 14553.96
## 4    3c 14525.20

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.16019    0.29038  -3.995 6.60e-05 ***
## phi    -0.05181    0.01563  -3.315 0.000927 ***
## alpha   0.95984    0.06610  14.521  < 2e-16 ***
## A       7.38315    0.65191  11.325  < 2e-16 ***
## k     126.92667    9.30383  13.642  < 2e-16 ***
## p       0.27138    0.02639  10.282  < 2e-16 ***
## s       1.97560    0.26706   7.398 1.77e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.323 on 3149 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.255e-06
##   (23 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93721, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8569, p-value = 0.0001148
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 136 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 147 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 819 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1944     2736.4                                 
## 2   1943     2648.3  1  88.031  64.585 1.588e-15 ***
## 3   1942     2525.2  1 123.122  94.687 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8215.337
## 2     2 8153.671
## 3     3 8062.982

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.99592    0.19686 -10.139   <2e-16 ***
## phi     0.12817    0.01434   8.939   <2e-16 ***
## alpha   0.83851    0.07880  10.641   <2e-16 ***
## A      13.36137    1.07860  12.388   <2e-16 ***
## k     137.33346   12.64614  10.860   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.14 on 1942 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.946e-06
##   (16 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1942     2525.2                                
## 2   1941     2504.1  1 21.118  16.369 5.417e-05 ***
## 3   1941     2521.5  0  0.000                      
## 4   1940     2491.7  1 29.802  23.204 1.570e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8062.982
## 2    3a 8048.631
## 3    3b 8062.103
## 4    3c 8040.954

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.98380    0.19705 -10.067  < 2e-16 ***
## phi     0.12772    0.01428   8.947  < 2e-16 ***
## alpha   0.84477    0.07666  11.020  < 2e-16 ***
## A      11.14578    1.06201  10.495  < 2e-16 ***
## k     130.79304   13.97929   9.356  < 2e-16 ***
## p       0.16266    0.03221   5.050 4.84e-07 ***
## s       1.64253    0.23847   6.888 7.63e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.133 on 1940 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.264e-06
##   (16 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9432, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.559, p-value = 0.119
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 83 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 90 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 993 row(s) containing missing values (geom_path).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    359     156.17                                 
## 2    358     152.35  1  3.8252  8.9887  0.002906 ** 
## 3    357     137.98  1 14.3704 37.1815 2.796e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 822.1395
## 2     2 815.1626
## 3     3 781.2972

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -2.05106    0.34195  -5.998 4.90e-09 ***
## phi     0.05371    0.02230   2.409   0.0165 *  
## alpha   0.81606    0.11897   6.859 3.06e-11 ***
## A      11.88674    2.36632   5.023 8.04e-07 ***
## k     196.34353   47.26084   4.154 4.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6217 on 357 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.533e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    357     137.98                          
## 2    356     137.27  1 0.70579  1.8304 0.1769
##   model      AIC
## 1     3 781.2972
## 2    3a 781.4408
## 3    3b 780.7006
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -2.036e+00  3.455e-01  -5.893 8.78e-09 ***
## phi    5.390e-02  2.227e-02   2.420    0.016 *  
## alpha  8.125e-01  1.191e-01   6.820 3.91e-11 ***
## A      1.617e+02  1.587e+03   0.102    0.919    
## k      1.958e+04  3.033e+05   0.065    0.949    
## s      7.028e-01  1.607e-01   4.373 1.61e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6203 on 356 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 8.71e-07

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9698, p-value = 7.756e-07
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.15594, p-value = 0.8761
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 15 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1316 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1708     1232.3                                
## 2   1707     1210.2  1 22.129  31.213 2.686e-08 ***
## 3   1706     1119.5  1 90.733 138.270 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4418.632
## 2     2 4389.628
## 3     3 4258.286

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.83743    1.05906   0.791    0.429    
## phi    0.09908    0.01294   7.656 3.18e-14 ***
## alpha  0.72719    0.05181  14.036  < 2e-16 ***
## A      1.83390    0.36253   5.059 4.68e-07 ***
## k     34.99648    5.27052   6.640 4.20e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8101 on 1706 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.455e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1706     1119.5                                
## 2   1705     1093.8  1 25.708  40.074 3.119e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4258.286
## 2    3a 4220.536
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.19875    1.18352   1.013   0.3113    
## phi     0.10174    0.01276   7.971 2.85e-15 ***
## alpha   0.73681    0.05033  14.640  < 2e-16 ***
## A       4.97281    2.69680   1.844   0.0654 .  
## k     594.83063  458.19282   1.298   0.1944    
## p       0.11960    0.05369   2.228   0.0260 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8009 on 1705 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.114e-07

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90717, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.55, p-value = 2.857e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 67 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 67 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1288 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   2623     2316.2                                
## 2   2622     2310.0  1   6.161   6.9935 0.00823 ** 
## 3   2621     2046.0  1 264.004 338.1952 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8369.361
## 2     2 8364.366
## 3     3 8047.671

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.26356    0.30114  -4.196 2.81e-05 ***
## phi    0.03588    0.01468   2.445   0.0146 *  
## alpha  0.95036    0.04423  21.489  < 2e-16 ***
## A      5.98323    0.62056   9.642  < 2e-16 ***
## k     82.21307    7.86354  10.455  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8835 on 2621 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 8.229e-06
##   (23 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2621     2046.0                                
## 2   2620     1909.3  1 136.75  187.65 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8047.671
## 2    3a 7868.020
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      -1.32429    0.27714  -4.778 1.86e-06 ***
## phi      0.02949    0.01413   2.087    0.037 *  
## alpha    0.92831    0.04313  21.521  < 2e-16 ***
## A       43.24977   35.26058   1.227    0.220    
## k     2281.03867 2086.52516   1.093    0.274    
## p        0.02976    0.02304   1.292    0.197    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8537 on 2620 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 7.946e-06
##   (23 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90185, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.4344, p-value = 1.051e-13
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 104 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 112 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1269 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1672     1976.4                              
## 2   1671     1975.6  1   0.811   0.686 0.4076    
## 3   1670     1717.1  1 258.478 251.384 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6547.760
## 2     2 6549.072
## 3     3 6316.200

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.664811   0.956615   0.695    0.487    
## phi    0.002048   0.018148   0.113    0.910    
## alpha  1.010251   0.055489  18.206  < 2e-16 ***
## A      4.270907   0.794280   5.377 8.64e-08 ***
## k     45.022078   4.833813   9.314  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.014 on 1670 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.412e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1670     1717.1                                
## 2   1669     1625.4  1 91.741  94.203 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model     AIC
## 1     3 6316.20
## 2    3a 6226.23
## 3    3b      NA
## 4    3c      NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.912e-01  8.705e-01   0.564 0.572686    
## phi   6.384e-03  1.762e-02   0.362 0.717251    
## alpha 9.850e-01  5.397e-02  18.250  < 2e-16 ***
## A     9.893e+00  2.669e+00   3.707 0.000217 ***
## k     4.404e+02  1.477e+02   2.981 0.002917 ** 
## p     1.201e-01  2.004e-02   5.992 2.53e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9868 on 1669 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.68e-06

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91305, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8628, p-value = 0.0001121
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 70 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 70 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1219 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    359     279.44                                 
## 2    358     279.00  1  0.4466  0.5731    0.4495    
## 3    357     256.62  1 22.3752 31.1276 4.782e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 993.7167
## 2     2 995.1377
## 3     3 966.8751

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.30924    1.46617  -0.211 0.833073    
## phi    0.01064    0.03218   0.331 0.741036    
## alpha  0.76868    0.12107   6.349 6.58e-10 ***
## A      2.55364    0.81480   3.134 0.001867 ** 
## k     36.20697   10.23649   3.537 0.000458 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8478 on 357 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.941e-06

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    357     256.62                          
## 2    356     256.50  1 0.11926  0.1655 0.6844
## 3    356     256.62  0 0.00000               
## 4    355     255.90  1 0.71939  0.9980 0.3185
##   model      AIC
## 1     3 966.8751
## 2    3a 968.7068
## 3    3b 968.8749
## 4    3c 969.8587

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.30924    1.46617  -0.211 0.833073    
## phi    0.01064    0.03218   0.331 0.741036    
## alpha  0.76868    0.12107   6.349 6.58e-10 ***
## A      2.55364    0.81480   3.134 0.001867 ** 
## k     36.20697   10.23649   3.537 0.000458 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8478 on 357 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.941e-06

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92291, p-value = 1.076e-12
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.1853, p-value = 0.02887
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 13 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 13 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 1350 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	3a
212	Laurentian Mixed Forest	3a
221	Eastern Broadleaf Forest	3a
222	Midwest Broadleaf Forest	3a
223	Central Interior Broadleaf Forest	3
231	Southeastern Mixed Forest	3a
232	Outer Coastal Plain Mixed Forest	3c
234	Lower Mississippi Riverine Forest	3b
242	Pacific Lowland Mixed Forest	3a
251	Prairie Parkland (Temperate)	3a
255	Prairie Parkland (Subtropical)	NA
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	1
313	Colorado Plateau Semi-Desert	3c
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	NA
332	Great Plains Steppe	3a
341	Intermountain Semi-Desert and Desert	NA
342	Intermountain Semi-Desert	3
411	Everglades	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	3c
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	3
M223	Ozark Broadleaf Forest Meadow	3
M231	Ouachita Mixed Forest	3
M242	Cascade Mixed Forest	3c
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	3c
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	3b
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	3a
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3a
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3a
M334	Black Hills Coniferous Forest	3
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	NA

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	alpha	alpha.2.5	alpha.97.5	A	A.2.5	A.97.5	k	k.2.5	k.97.5
211	Northeastern Mixed Forest	east	6806	2847	0.0032341	-0.2756589	0.2821270	0.0196353	0.0111317	0.0281389	0.6304287	0.5726594	0.6881979	3.741260	3.5207886	3.961732	13.6997192	9.654695e+00	1.774474e+01
212	Laurentian Mixed Forest	east	18775	8891	0.5875552	0.3473638	0.8277467	0.0296065	0.0242962	0.0349169	0.8146466	0.7753388	0.8539544	3.134793	2.9862625	3.283323	29.2068568	2.538519e+01	3.302852e+01
221	Eastern Broadleaf Forest	east	7170	3490	-1.4353661	-1.5984164	-1.2723159	0.0067019	-0.0020867	0.0154906	0.6856822	0.6180803	0.7532841	7.601341	6.8772003	8.325482	99.3306519	6.020173e+01	1.384596e+02
222	Midwest Broadleaf Forest	east	4877	2401	-0.3832030	-0.7169445	-0.0494615	0.0181604	0.0039591	0.0323617	0.7924866	0.7179678	0.8670053	6.608906	5.8836321	7.334179	112.2105442	8.332827e+01	1.410928e+02
223	Central Interior Broadleaf Forest	east	8783	3725	-1.3866092	-1.5488155	-1.2244028	-0.0223289	-0.0329539	-0.0117039	0.6406604	0.5695074	0.7118133	6.472890	6.1175357	6.828244	42.0437174	3.673232e+01	4.735511e+01
231	Southeastern Mixed Forest	east	12347	5691	-0.1868506	-0.3779020	0.0042008	-0.0021302	-0.0101573	0.0058968	0.8401828	0.8007650	0.8796007	5.596113	5.3550385	5.837187	8.7746004	5.594570e+00	1.195463e+01
232	Outer Coastal Plain Mixed Forest	east	12470	6101	-0.2904340	-0.5045303	-0.0763378	-0.0008326	-0.0096675	0.0080024	0.8287948	0.7872407	0.8703488	5.513232	5.1838221	5.842643	24.1803371	1.997348e+01	2.838720e+01
234	Lower Mississippi Riverine Forest	east	1265	714	1.6092105	-0.5934506	3.8118716	-0.0257637	-0.0665282	0.0150008	0.7689237	0.6117706	0.9260769	4.138424	2.3170892	5.959759	11.6455855	-5.094672e-01	2.380064e+01
242	Pacific Lowland Mixed Forest	pacific	81	81	-0.9525826	-3.5499334	1.6447682	0.0699013	-0.0266063	0.1664088	0.8122504	0.3308180	1.2936827	22.297206	-32.5184393	77.112850	1188.9871458	-3.496157e+03	5.874131e+03
251	Prairie Parkland (Temperate)	east	1797	809	-0.8248859	-1.3168379	-0.3329340	0.0263597	0.0060061	0.0467134	0.3946292	0.2215338	0.5677246	19.869740	-28.7842324	68.523713	1228.2693363	-2.646294e+03	5.102833e+03
255	Prairie Parkland (Subtropical)	pacific	663	293	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
261	California Coastal Chaparral Forest and Shrub	pacific	24	24	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	155	155	-1.5581294	-3.7834605	0.6672017	NA	NA	NA	NA	NA	NA	8.593004	2.7659460	14.420063	-0.2271304	-9.928109e+00	9.473848e+00
313	Colorado Plateau Semi-Desert	interior west	215	215	-1.1547223	-3.0100569	0.7006123	-0.0954482	-0.2296346	0.0387382	0.8440010	0.3810746	1.3069274	2.685375	0.8808844	4.489866	109.8436325	5.821653e+01	1.614707e+02
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	304	240	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
332	Great Plains Steppe	interior west	195	106	0.2618211	-2.5849626	3.1086047	0.0242467	-0.0386217	0.0871152	0.7102473	0.2168739	1.2036208	5.215762	1.2476133	9.183912	142.5985631	-1.940133e+01	3.045985e+02
341	Intermountain Semi-Desert and Desert	interior west	62	62	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	interior west	121	120	2.6645524	-9.2968369	14.6259417	-0.0013691	-0.1001661	0.0974279	0.8820840	0.4328260	1.3313421	3.485949	-2.2893846	9.261282	119.5107492	2.766230e+01	2.113592e+02
411	Everglades	east	93	61	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6729	2989	0.5510365	0.2142071	0.8878658	0.0139686	0.0061589	0.0217782	0.6521370	0.6004297	0.7038444	3.030047	2.8287707	3.231323	11.4695217	7.432149e+00	1.550689e+01
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8034	3700	-0.7457552	-0.9584146	-0.5330959	-0.0040380	-0.0149685	0.0068926	0.7062759	0.6097832	0.8027687	5.088126	4.8003928	5.375858	13.2042744	9.988285e+00	1.642026e+01
M223	Ozark Broadleaf Forest Meadow	east	883	343	2.7573280	-0.0624472	5.5771032	-0.0413414	-0.0848804	0.0021975	0.9006835	0.6245979	1.1767690	2.041119	1.2648198	2.817419	14.5796336	2.640085e+00	2.651918e+01
M231	Ouachita Mixed Forest	east	988	481	1.5999846	-0.7745286	3.9744977	0.0657658	0.0155696	0.1159619	0.7292396	0.4963788	0.9621003	2.180454	1.3678621	2.993047	3.1968983	2.747197e-01	6.119077e+00
M242	Cascade Mixed Forest	pacific	3179	3176	-1.1601936	-1.7295372	-0.5908500	-0.0518086	-0.0824529	-0.0211644	0.9598361	0.8302333	1.0894389	7.383150	6.1049325	8.661366	126.9266652	1.086845e+02	1.451689e+02
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	1963	1963	-1.9838043	-2.3702620	-1.5973466	0.1277165	0.0997199	0.1557131	0.8447735	0.6944352	0.9951119	11.145784	9.0629800	13.228589	130.7930407	1.033770e+02	1.582090e+02
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	19	19	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	362	362	-2.0360162	-2.7154342	-1.3565981	0.0539041	0.0101067	0.0977015	0.8124616	0.5781913	1.0467319	161.727835	-2958.5278536	3281.983523	19582.5578448	-5.768110e+05	6.159761e+05
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	1711	1711	1.1987530	-1.1225524	3.5200584	0.1017445	0.0767105	0.1267786	0.7368088	0.6380970	0.8355206	4.972806	-0.3165882	10.262201	594.8306305	-3.038487e+02	1.493510e+03
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	2649	2648	-1.3242877	-1.8677141	-0.7808613	0.0294913	0.0017781	0.0572045	0.9283088	0.8437272	1.0128904	43.249774	-25.8916364	112.391184	2281.0386662	-1.810366e+03	6.372443e+03
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	1675	1675	0.4911505	-1.2162515	2.1985525	0.0063836	-0.0281853	0.0409525	0.9849811	0.8791243	1.0908378	9.892989	4.6586997	15.127278	440.4073066	1.506162e+02	7.301984e+02
M334	Black Hills Coniferous Forest	interior west	362	170	-0.3092380	-3.1926440	2.5741681	0.0106444	-0.0526491	0.0739379	0.7686805	0.5305895	1.0067715	2.553637	0.9512291	4.156044	36.2069653	1.607556e+01	5.633837e+01
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	213	213	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 14 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 13 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  -0.3033411
## 2       pacific  -1.3875003
## 3          east  -0.1801957
## 4 interior west  -0.1751151

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.012449470
## 2       pacific  0.016132330
## 3          east  0.007881616
## 4 interior west  0.035209433

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.7672651
## 2       pacific      0.8384614
## 3          east      0.7492007
## 4 interior west      0.8146180

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   8.429589
## 2       pacific   8.514766
## 3          east   5.188456
## 4 interior west  26.483097

K (stand biomass at half biomss G in Mg/ha)

##          region weighted.k
## 1     entire US  325.45914
## 2       pacific  132.84234
## 3          east   55.87903
## 4 interior west 1977.47017

FIA - NLS Models: Biomass Growth vs. Biomass

JAH

2022-10-13

Background

211 - Northeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

model selection 2